发表机构
Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR); Singapore University of Technology and Design; Centre for Quantum Technologies, National University of Singapore; Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University（先进智能与计算研究所，科学、技术与研究局; 新加坡科技设计大学; 新加坡国立大学量子技术中心; 南洋理工大学物理与数学科学学院南洋量子枢纽）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出BARC码的一般多项式框架，利用复多项式解集对称性构造相干态叠加码，满足近似Knill-Laflamme条件，并给出椭球与六角码实例及噪声鲁棒性上界。
AI 中文摘要
我们引入了一个代数框架，用于构建一类新的量子纠错码——玻色子代数受限星座（BARC）码。码态是相干态星座的有限叠加，这些星座受多元复多项式系统解集的对称性约束。这些约束与光子增益和光子损失误差相关联，从而对此类误差施加近似的Knill-Laflamme条件。对于等权星座点，我们推导了各点之间最小几何间隔的上界，这指示了码的噪声鲁棒性。在单模情形下，我们利用正交群对称性刻画二次多项式解集，以获得显式的椭球和六角BARC码。我们通过纯损耗噪声下最优恢复的纠缠保真度，将这些族的代表性实例与球形码和数值积分（cubature）码进行了基准比较。
英文摘要
We introduce an algebraic framework for constructing a new class of quantum error-correcting codes, bosonic algebraically-restricted constellation (BARC) codes. The code states are finite superpositions of coherent-state constellations constrained by symmetries of solution sets to multivariate complex polynomial systems. The constraints are associated with photon-gain and photon-loss errors, thereby imposing approximate Knill--Laflamme conditions for such errors. For equally-weighted constellation points, we derive upper bounds on the minimum geometric separation between points, indicating how noise-resilient the code is. In the single-mode case, we characterize degree-two polynomial solution sets using an orthogonal group symmetry to obtain explicit ellipsoidal and hexagonal BARC codes. We benchmark representative instances of these families against spherical and cubature codes using the entanglement fidelity with optimal recovery under pure-loss noise.
Comments96 pages
